# Thread: need help with this proof

1. ## need help with this proof

Hi ppl, pretty new to maths. picked up a discrete mathematics unit this semester at uni for something a little different. got a quick question.

Question: given that n is an integer, prove that n is even if and only if 9n2 + 4n - 11 is odd.

Now, i already know that the above is true. just wondering what is the general accepted format to answer this type of question? i dont know what my answer is supposed to look like so could someone maybe do a quick demonstration proof of this question so i can see how this works?

2. Originally Posted by dogma
Hi ppl, pretty new to maths. picked up a discrete mathematics unit this semester at uni for something a little different. got a quick question.

Question: given that n is an integer, prove that n is even if and only if 9n2 + 4n - 11 is odd.

Now, i already know that the above is true. just wondering what is the general accepted format to answer this type of question? i dont know what my answer is supposed to look like so could someone maybe do a quick demonstration proof of this question so i can see how this works?
$9n^2+4n-11\equiv n^2-1\text{ mod }2$

Clearly then $n\text{ even}\Leftrightarrow n\equiv0\text{ mod }2\Leftrightarrow n^2-1\equiv1\text{ mod }2\Leftrightarrow 9n^2+4n-11\text{ odd}$

3. cheers